Finite Group Databasebeta

← #14326356

Subgroups — #14326356

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D15C211yesmaximal, characteristic
2C2×#91561C211yesmaximal, characteristic
3C2×#91386C211yesmaximal, characteristic, complemented
4C5×#4951C211yesmaximal, characteristic, complemented
5C3×#65240C211yesmaximal, characteristic, complemented
6#11749502C211yesmaximal, characteristic
7#11749481C211yesmaximal, characteristic, complemented
8#11749480C211yesmaximal, characteristic, complemented
9#11748902C211yesmaximal, characteristic, complemented
10#11748898C211yesmaximal, characteristic, complemented
11#11748881C211yesmaximal, characteristic, complemented
12#11748875C211yesmaximal, characteristic, complemented
13#11748799C211yesmaximal, characteristic, complemented
14#11748670C211yesmaximal, characteristic, complemented
15#11748606C211yesmaximal, characteristic, complemented
16#10607563—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C22⋊C4×D15C418yescomplemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35#91561—24no—
36C2×#6669C2211yescharacteristic, complemented
37C2×#6669C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91386—24no—
47C5×C3⋊#95C2211yescharacteristic, complemented
48C5×C3⋊#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#75832—51nomaximal, Hall
56C2×D5×C22⋊C4—31no—
57C2×D5×C22⋊C4—31no—
58C2×#4018—31no—
59C5×#388—31no—
60#65278—31no—
61#65276—31no—
62#65244—31no—
63#65240D311yescharacteristic, complemented
64#65234—31no—
65#65233—31no—
66C4×#685—31no—
67#64957—31no—
68#64955—31no—
69#64955—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15—22no—
73C23×D15—22no—
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15C2×C414yes—
79C23×D15C2311yescharacteristic
80C23×D15C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C4×D15—22no—
86C2×C4×D15—22no—
87C2×C4×D15—41no—
88C2×C4×D15—41no—
89C2×C4×D15C2×C414yescomplemented
90C2×C4×D15C2×C414yescomplemented
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—22no—
102C2×#1200—22no—
103C2×#1200—41no—
104C2×#1200—41no—
105C3×C5×C22⋊C4C2×C414yescomplemented
106#6719C2×C414yescomplemented
107#6714C2×C414yes—
108#6714C2×C414yes—
109C5×#217—22no—
110C5×#217—41no—
111C5×C4⋊Dic3—41no—
112C4×C5×Dic3—22no—
113C3×C22⋊Dic5—22no—
114C3×C22⋊Dic5—41no—
115C3×C4⋊Dic5—41no—
116C3×C4×Dic5—22no—
117#6669—22no—
118#6669—22no—
119#6667—22no—
120#6667—22no—
121#6667—22no—
122#6667—22no—
123#6667—22no—
124#6667D414yes—
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C2×D3×C22⋊C4—51no—
128C2×D3×C22⋊C4—51no—
129C2×#872—51no—
130C3×#388—51no—
131#4989—51no—
132#4987—51no—
133#4955—51no—
134#4951D511yescharacteristic, complemented
135#4945—51no—
136#4944—51no—
137C4×(C2×D3)⋊C4—51no—
138#4668—51no—
139#4666—51no—
140#4666—51no—
141#4664—51no—
142C24×D5—31no—
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C42×C5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5C2×D311yescharacteristic
154C2×C22⋊Dic5C2×D311yescharacteristic
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×C4⋊Dic5C2×D311yescharacteristic, complemented
164C2×#683—31no—
165C2×#683—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5C2×D311yescharacteristic, complemented
169D5×C22⋊C4—38no—
170D5×C22⋊C4—64no—
171#4018—64no—
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic, complemented
179#3963C2×D311yescharacteristic, complemented
180#2342—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—28no—
198C22×D15—28no—
199C22×D15—44no—
200C22×D15—44no—
201C22×D15—44no—
202C22×D15—44no—
203C22×D15—44no—
204C22×D15C22×C412yes—
205C22×D15C22×C412yes—
206C22×D15C2×D412yes—
207C22×D15#4112yes—
208C22×D15#4112yes—
209C22×D15#4112yes—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C22×C412yes—
215C2×C3×C4×C5C22×C412yes—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15C22×C412yes—
221C2×Dic15C22×C412yes—
222C4×D15—28no—
223C4×D15—44no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3C2×D412yes—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C2×D412yes—
248#1200—44no—
249#1200—44no—
250C24×D3—51no—
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C42—51no—
260C2×#217—51no—
261C2×#217C2×D511yescharacteristic
262C2×#217C2×D511yescharacteristic
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×C4⋊Dic3C2×D511yescharacteristic, complemented
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3C2×D511yescharacteristic, complemented
277D3×C22⋊C4—58no—
278D3×C22⋊C4—104no—
279#872—104no—
280C3×#95—51no—
281C3×#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5C22×D311yescharacteristic
289C23×D5—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—62no—
296C23×D5—121no—
297C23×D5—121no—
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5C22×D311yescharacteristic
307C22×Dic5C22×D311yescharacteristic
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×C4×D5—34no—
311C2×C4×D5—34no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—121no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—121no—
323C5×C22⋊C4—62no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4C4×D314yescomplemented
326C42×C5—62no—
327C22⋊Dic5—22no—
328C22⋊Dic5—34no—
329C22⋊Dic5—41no—
330#685—34no—
331#685—34no—
332#685—34no—
333#685—62no—
334#685—62no—
335#685—62no—
336#685—62no—
337#685—62no—
338C4⋊Dic5—41no—
339#683—62no—
340#683—62no—
341C4×Dic5—22no—
342C4×Dic5—121no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—31no—
348#388—51no—
349#388—151no—
350#388—151no—
351#385—151no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—151no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×D15—22no—
374C2×D15—22no—
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—416no—
386C2×D15#11714yescomplemented
387C2×D15C4×D414yes—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390Dic15—22no—
391Dic15—22no—
392C3×Dic5—22no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C5×Dic3—22no—
397C5×Dic3—41no—
398C5×Dic3—41no—
399C5×Dic3—41no—
400C24×C3C22×D511yescharacteristic
401C23×D3—51no—
402C23×D3—51no—
403C23×D3—54no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—102no—
408C23×D3—201no—
409C23×D3—201no—
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3C22×D511yescharacteristic
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—54no—
423C2×C4×D3—54no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—102no—
430C2×C4×D3—201no—
431C2×C4×D3—201no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C3×C4⋊C4—201no—
435C3×C22⋊C4—102no—
436C3×C22⋊C4—201no—
437C3×C22⋊C4C4×D514yescomplemented
438C3×C42—102no—
439#217—22no—
440#217—41no—
441#217—54no—
442(C2×D3)⋊C4—54no—
443(C2×D3)⋊C4—54no—
444(C2×D3)⋊C4—54no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—102no—
447(C2×D3)⋊C4—102no—
448(C2×D3)⋊C4—102no—
449(C2×D3)⋊C4—102no—
450C4⋊Dic3—41no—
451Dic3⋊C4—102no—
452Dic3⋊C4—102no—
453C4×Dic3—22no—
454C4×Dic3—201no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C2×C4×D312yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—32no—
465C22×D5—32no—
466C22×D5—32no—
467C22×D5—32no—
468C22×D5—32no—
469C22×D5—32no—
470C22×D5—68no—
471C22×D5—68no—
472C22×D5—61no—
473C22×D5—61no—
474C22×D5—61no—
475C22×D5—61no—
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—61no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5—124no—
483C22×D5—124no—
484C22×D5—124no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—32no—
490C2×C4×C5—61no—
491C2×C4×C5—61no—
492C2×C4×C5—61no—
493C2×C4×C5—61no—
494C2×C4×C5—61no—
495C2×C4×C5—61no—
496C2×C4×C5—61no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5C2×C4×D312yes—
502C2×C4×C5C2×C4×D312yes—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—32no—
515C2×Dic5—32no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5D3×D412yes—
521C4×D5—68no—
522C4×D5—124no—
523C4×D5—124no—
524C4×D5—124no—
525C25—151no—
526C23×C4—151no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—158no—
544C2×C22⋊C4—151no—
545C2×C22⋊C4—151no—
546C2×C22⋊C4—151no—
547C2×C22⋊C4—151no—
548C2×C22⋊C4—151no—
549C2×C22⋊C4—304no—
550C2×C22⋊C4D3×D511yescharacteristic
551C2×C42—31no—
552C2×C42—51no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—31no—
557#95—51no—
558#95—51no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5—42no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571D15—24no—
572D15—24no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3C2×C4×D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—52no—
583C22×D3—52no—
584C22×D3—52no—
585C22×D3—52no—
586C22×D3—52no—
587C22×D3—108no—
588C22×D3—108no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—101no—
594C22×D3—101no—
595C22×D3—101no—
596C22×D3—101no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3—204no—
600C22×D3—204no—
601C22×D3—204no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—52no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4C2×C4×D512yes—
619C2×C3×C4C2×C4×D512yes—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3D4×D512yes—
638C4×D3—108no—
639C4×D3—204no—
640C4×D3—204no—
641C4×D3—204no—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×D3×D411yescharacteristic
651C22×C5#100411yescharacteristic
652C22×C5D3×#4111yescharacteristic
653C22×C5D3×#4111yescharacteristic
654C22×C5D3×#4111yescharacteristic
655C22×C5#100911yescharacteristic
656C2×D5—34no—
657C2×D5—34no—
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—62no—
670C2×D5—1216no—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—121no—
675C4×C5—121no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—41no—
679Dic5—41no—
680Dic5—41no—
681Dic5—62no—
682Dic5—62no—
683C24—151no—
684C24—151no—
685C24—154no—
686C24—302no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—601no—
691C24—601no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—302no—
706C22×C4—302no—
707C22×C4—302no—
708C22×C4—302no—
709C22×C4—302no—
710C22×C4—302no—
711C22×C4—601no—
712C22×C4—601no—
713C22×C4—601no—
714C22×C4—601no—
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—121no—
718C4⋊C4—201no—
719C4⋊C4—302no—
720C4⋊C4—302no—
721C22⋊C4—62no—
722C22⋊C4—102no—
723C22⋊C4—121no—
724C22⋊C4—154no—
725C22⋊C4—154no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—201no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—302no—
734C22⋊C4#120014yescomplemented
735C42—62no—
736C42—102no—
737C42—601no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3C22×C4×D511yescharacteristic
748C22×C3C2×D4×D511yescharacteristic
749C22×C3#414411yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C22×C3D5×#4111yescharacteristic
752C22×C3D5×#4111yescharacteristic
753C22×C3#414911yescharacteristic
754C2×D3—54no—
755C2×D3—54no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—102no—
766C2×D3—102no—
767C2×D3—102no—
768C2×D3—2016no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—102no—
772C3×C4—201no—
773C3×C4—201no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—41no—
777Dic3—41no—
778Dic3—41no—
779Dic3—102no—
780Dic3—102no—
781C2×C5—42no—
782C2×C5D3×#11711yescharacteristic
783C2×C5C4×D3×D411yescharacteristic
784C2×C5#554511yescharacteristic
785C2×C5#561211yescharacteristic
786C2×C5#565411yescharacteristic
787C2×C5#567911yescharacteristic
788C2×C5#570511yescharacteristic
789D5—64no—
790D5—64no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—152no—
798C23—152no—
799C23—152no—
800C23—152no—
801C23—152no—
802C23—152no—
803C23—308no—
804C23—308no—
805C23—301no—
806C23—301no—
807C23—301no—
808C23—301no—
809C23—301no—
810C23—301no—
811C23—301no—
812C23—301no—
813C23—604no—
814C23—604no—
815C23—604no—
816C23—604no—
817C23—604no—
818C23C2×#120012yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—32no—
825C2×C4—52no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—101no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—152no—
849C2×C4—152no—
850C2×C4—308no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—604no—
856C2×C4—604no—
857C2×C4—604no—
858C2×C4C2×#120012yes—
859C2×C4C2×#120012yes—
860C2×C3—42no—
861C2×C3D5×#11711yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6594611yescharacteristic
865C2×C3#6598811yescharacteristic
866C2×C3#6601311yescharacteristic
867C2×C3#6603911yescharacteristic
868D3—104no—
869D3—104no—
870C5#7583211yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—154no—
879C22—154no—
880C22—302no—
881C22—302no—
882C22—302no—
883C22—302no—
884C22—302no—
885C22—302no—
886C22—302no—
887C22—302no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—6016no—
893C22#9201611yescharacteristic
894C22#9201611yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22#9202411yescharacteristic
897C22#9202611yescharacteristic
898C22#9202711yescharacteristic
899C22C22×#120011yescharacteristic
900C4—22no—
901C4—22no—
902C4—62no—
903C4—102no—
904C4—121no—
905C4—121no—
906C4—121no—
907C4—201no—
908C4—201no—
909C4—201no—
910C4—302no—
911C4—302no—
912C3#1060756311yescharacteristic, complemented, Sylow
913C2—42no—
914C2—304no—
915C2—304no—
916C2#1175301511yescharacteristic
917C2#1175301911yescharacteristic
918C2#1175323711yescharacteristic
919C2#1175325611yescharacteristic
920C2#1175446111yescharacteristic
921C2D4×#120011yescharacteristic
922C2#1175492211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#91386C2semidirect
4. C5×#4951C2semidirect
5. C3×#65240C2semidirect
7. #11749481C2semidirect
8. #11749480C2semidirect
9. #11748902C2semidirect
10. #11748898C2semidirect
11. #11748881C2semidirect
12. #11748875C2semidirect
13. #11748799C2semidirect
14. #11748670C2semidirect
15. #11748606C2semidirect
26. C22⋊C4×D15C4semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
33. C2×C3×C4⋊Dic5C22semidirect
34. C2×C3×C4×Dic5C22semidirect
36. C2×#6669C22semidirect
37. C2×#6669C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. C5×C3⋊#95C22semidirect
48. C5×C3⋊#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
63. #65240D3semidirect
89. C2×C4×D15C2×C4semidirect
90. C2×C4×D15C2×C4semidirect
105. C3×C5×C22⋊C4C2×C4semidirect
106. #6719C2×C4semidirect
134. #4951D5semidirect
163. C2×C4⋊Dic5C2×D3semidirect
168. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
271. C2×C4⋊Dic3C2×D5semidirect
276. C2×C4×Dic3C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
325. C5×C22⋊C4C4×D3semidirect
386. C2×D15#117semidirect
437. C3×C22⋊C4C4×D5semidirect
734. C22⋊C4#1200semidirect
739. C3×C5#2342semidirect
870. C5#75832semidirect
912. C3#10607563semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C22⋊C4×D152
C2×#915612
C2×#913862
C5×#49512
C3×#652402
#117495022
#117494812
#117494802
#117489022
#117488982
#117488812
#117488752
#117487992
#117486702
#117486062
#106075633
#758325